Final answer to the problem
$x-1+\frac{2}{x-1}$
Got another answer? Verify it here!
Step-by-step Solution
Specify the solving method
1
Divide $x^2-2x+3$ by $x-1$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-1;}{\phantom{;}x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-1\overline{\smash{)}\phantom{;}x^{2}-2x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-1;}\underline{-x^{2}+x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{2}+x\phantom{;};}-x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n;}\underline{\phantom{;}x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}x\phantom{;}-1\phantom{;}\phantom{;}-;x^n;}\phantom{;}2\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$x-1+\frac{2}{x-1}$
Final answer to the problem
$x-1+\frac{2}{x-1}$